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Analisis Kemampuan Representasi Matematis Mahasiswa Melalui Perkuliahan Geometri Analitik Topik Garis Dihna, Elza Rahma; Sudihartinih, Eyus
JIPM (Jurnal Ilmiah Pendidikan Matematika) Vol 11, No 2 (2023)
Publisher : Universitas PGRI Madiun

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25273/jipm.v11i2.12443

Penelitian ini bertujuan untuk mendeskripsikan kemampuan representasi matematis mahasiswa dalam menyelesaikan soal geometri analitik. Jenis penelitian yang digunakan dalam penelitian ini adalah penelitian deskriptif dengan menggunakan pendekatan kualitatif. Partisipan pada penelitian ini adalah 12 orang mahasiswa program studi pendidikan matematika yang mengontrak mata kuliah geometri analitik. Instrumen soal yang digunakan pada penelitian ini adalah tiga butir soal uraian pada topik garis. Pada hasil penelitian ini didapatkan bahwa kemampuan representasi matematis mahasiswa calon guru pada mata kuliah geometri analitik dalam topik garis masih kurang. Dari ketiga indikator kemampuan representasi matematis, didapatkan bahwa partisipan dapat dengan baik menampilkan reprsentasi visual berupa gambar atau grafik, kemudian untuk representasi persamaan atau ekspresi matematis dapat dicapai dengan baik oleh hampir seluruh partisipan. Dan indikator yang paling sedikit dicapai oleh partisipan adalah indikator representasi verbal pada indikator ini hanya ada dua partisipan yang mampu menampilkannya.

Markov Chain Method for Calculating Insurance Premiums Dihna, Elza Rahma; Ismail, Muhammad Iqbal Al-Banna
International Journal of Quantitative Research and Modeling Vol 5, No 4 (2024)
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijqrm.v5i4.817

This study applies the Markov Chain method to calculate insurance premiums based on the dynamic health status of policyholders over time. The model considers three health states Healthy, Mild Illness, and Severe Illness each associated with a specific insurance premium. The transition probabilities between these states are represented in a transition matrix, capturing the likelihood of a policyholder remaining in their current health state or transitioning to another state in a given period. Using this approach, the steady-state distribution, which reflects the long-term probabilities of being in each health state, is calculated. This distribution is then used to determine the expected monthly premium by taking a weighted average of the premiums for each state. The methodology incorporates real-world scenarios where a policyholder's health condition may change over time, impacting the premiums they are required to pay. The Markov Chain model provides an effective framework for estimating these premiums by considering the "memoryless" nature of health state transitions, where future states depend only on the current state and not on prior health history. By solving the steady-state equations pi P=pi and ensuring the total probabilities sum to one, the model yields a robust estimation of long-term health state distributions. These distributions, combined with the associated premiums, produce an accurate calculation of expected insurance costs. The results demonstrate the flexibility and accuracy of the Markov Chain method in assessing risks and setting premiums. Insurers benefit from this approach as it enables dynamic pricing strategies tailored to individual risk profiles. For policyholders, the model provides transparency in understanding how health status influences premiums. Overall, this study highlights the practicality of using Markov Chains in health insurance pricing and underscores their importance in creating equitable and sustainable insurance systems.

Numerical Solution of the Time-Fractional Black-Scholes Equation and Its Application to European Option Pricing Dihna, Elza Rahma; Rusyaman, Endang; Sukono, Sukono
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.35248

The classical Black-Scholes model is widely used in option pricing but relies on idealized assumptions such as constant volatility and memoryless market dynamics, which limit its accuracy in capturing real-world financial behavior. To overcome these limitations, the time-fractional Black-Scholes model incorporates a fractional-order derivative—specifically the Caputo derivative—which introduces memory effects and accommodates time-varying volatility. This study focuses on numerically solving the time-fractional Black-Scholes equation using the finite difference method (FDM) and applying the results to the pricing of European call options. The model is discretized using an implicit finite difference scheme to ensure stability and accuracy over the time domain. Numerical simulations are conducted for various values of the fractional order α, illustrating that the option price is sensitive to the fractional parameter. Lower values of α tend to increase option prices, highlighting the influence of memory effects on pricing behavior. The results confirm that the finite difference method is an effective numerical tool for solving fractional partial differential equations and demonstrate that the fractional Black-Scholes model offers improved flexibility and realism in option valuation, particularly in markets characterized by irregular volatility and non-Markovian features.

Markov Chain Method for Calculating Insurance Premiums Dihna, Elza Rahma; Ismail, Muhammad Iqbal Al-Banna
International Journal of Quantitative Research and Modeling Vol. 5 No. 4 (2024)
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijqrm.v5i4.817

This study applies the Markov Chain method to calculate insurance premiums based on the dynamic health status of policyholders over time. The model considers three health states Healthy, Mild Illness, and Severe Illness each associated with a specific insurance premium. The transition probabilities between these states are represented in a transition matrix, capturing the likelihood of a policyholder remaining in their current health state or transitioning to another state in a given period. Using this approach, the steady-state distribution, which reflects the long-term probabilities of being in each health state, is calculated. This distribution is then used to determine the expected monthly premium by taking a weighted average of the premiums for each state. The methodology incorporates real-world scenarios where a policyholder's health condition may change over time, impacting the premiums they are required to pay. The Markov Chain model provides an effective framework for estimating these premiums by considering the "memoryless" nature of health state transitions, where future states depend only on the current state and not on prior health history. By solving the steady-state equations pi P=pi and ensuring the total probabilities sum to one, the model yields a robust estimation of long-term health state distributions. These distributions, combined with the associated premiums, produce an accurate calculation of expected insurance costs. The results demonstrate the flexibility and accuracy of the Markov Chain method in assessing risks and setting premiums. Insurers benefit from this approach as it enables dynamic pricing strategies tailored to individual risk profiles. For policyholders, the model provides transparency in understanding how health status influences premiums. Overall, this study highlights the practicality of using Markov Chains in health insurance pricing and underscores their importance in creating equitable and sustainable insurance systems.

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